Numerology is an arcane study of the purported mystical relationship between numbers and the character or action of physical objects and living things.

Numerology and numerological divination was popular among early mathematicians such as Pythagoras, but is no longer considered to be part of mathematics.
This is similar to the historical development of astronomy from astrology, and that of chemistry from alchemy.

In numerological divination, a student of the field will use the name, birthdate and birthtime of an individual to analyze and define something of the personality and propensities of that individual. Specific numbers are also assigned to the letters of the alphabet. In this way, names of people, places and things can be assigned numerical values, thus giving them meaning in a numerologic context. The asserted basis of numerology is that every object, place or being in the universe has a characteristic vibration, usually imperceptible to the human senses, and that the application of numerology to the thing being addressed can help to ascertain the characteristic vibration or vibrations which apply to it, thereby revealing something of its essence. Classic numerology resolves all numbers related to an item down to a single digit, 0-9 or 1-9, plus the "master numbers" 11 and 22. The number 324, for instance, would be resolved by adding 3+2+4 to arrive at 9. 12 and 16, appearing together in a date, would resolve to 10, hence 1, no matter in which order the elements are added.

The basis of the belief that dates and times have numerologic significance appears to be that underlying vibrations of the universe as a whole occur in regular cycles and that things created or changed at one or another point in these cycles will express the properties which the vibrations at that point in the cycle create. It is less clear how names, words and appelations would follow such a rule. One theory put forward by some numerologists is that persons who name things are subtly affected by universal vibrations to assign appropriate names which harmonize with the vibrations of the thing named.

Another question which has been asked relative to the numerological significance of words is how, if letters can be assigned numbers, things can have a uniform numerological identity when they are named differently in different languages and with different alphabets. For example, the numerologic value for "shirt" in english would be 8. The same item in Spanish would be "camisa," a 6 in numerology. A clear and uniform explanation of such inconsistency has not been offered.

To date, there is no known scientific verification for the validity of claimed numerological principles. Numerology has thus been classified as a pseudoscience, and most scientists regard it as either deluded quackery or deliberate fraud. True science, as recognized in modern society, is based on the scientific method and requires that assertions answer to the regular and replicable use of this method to be considered as scientifically verifiable fact.

Numerologists reply that their study does not answer to science as the mechanisms of interaction between universal vibration and gross physical things are too subtle to be detected, measured or quantified by tools currently available to science. However, given that numerologists make predictions about observable events, scientists would argue that the simultaneous claim that science cannot detect any effects is illogical. Empirical observations relating to the regular and predictable mathematical relationships between things in the universe are pointed to as evidence of a numerological fabric underlying all things. However, such observations give no direct support to numerology's claims.

Numerology is by no means a unified study. Proponents of its veracity may be generally divided into three schools. With limited elaboration:

Numerology is true by Divine fiat and contains clues placed into the fabric of the universe by the Almighty for the enlightened to decipher, thereby bringing them closer to unity with a Grand Plan.

Numerology is true because of universal spiritual agreement between all life on one level or another. And because the Universe is the product of the mean (as in statistical mean) agreement between all of life everywhere, the agreement on mathematical regularity in the universe creates a Numerological sub-fabric throughout the universe.

Numerology is true because it is a reflection of Natural Law, giving clues to the state of a complex of vibrations which regulate function and existence in the universe. The failure of modern science to verify this fact is merely a reflection of insufficient advances in science. After all, science once believed all matter was composed of earth, air, fire and water in different combinations. If and when science is sufficiently advanced, it will be able to verify the truth of numerology.

Pythagoras and other philosophers of the time believed that because mathematical concepts were more "practical" (easier to regulate and classify) than physical ones, they had greater actuality. This is an idea in harmony with philosophical pragmatism and a choice for permanent concepts over changeable physicality.

St. Augustine of Hippo in A.D. 354 - 430 wrote " Numbers are the Universal language offered by the deity to humans as confirmation of the truth." Similar to Pythagoras, he too believed that everything had numerical relationships and it was up to the mind to seek and investigate the secrets of these relationships or have them revealed by divine grace.

In 325 A.D., following the First Council of Nicaea, departures from the beliefs of the state Church were classified as civil violations within the Roman Empire. Numerology had not found favor with the Christian authority of the day. It was assigned to the field of unapproved beliefs along with astrology and other forms of divination and "magic." Through this religious purging, the spiritual significance assigned to the heretofore "sacred" numbers began to disappear. In spite of this suppression there were still many devout believers, who kept the secret knowledge locked away.

A claim of numerology is that its practitioners, through empirical observation and investigation, have concluded that through the study of numbers man can uncover hidden aspects of himself and the universe.